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A rollercoaster cart that has a mass of 4500 kg has 67.5 kJ (kilojoules), or 67,500 J (joules), of gravitational potential
energy. What is its height above the ground?
PT.2
The same 4500 kg rollercoaster cart is moving with 63.0 kJ (kilojoules), or 63,000 J (joules), of kinetic energy at the
bottom of its biggest hill. What is its velocity?


Sagot :

Answer: The height of rollercoaster cart above the ground is 1.53 m.

The velocity of rollercoaster cart is 5.29 m/s.

Explanation:

Potential energy is the energy occupied by a substance due to its position. Formula for potential energy is as follows.

P.E = mgh

where,

m = mass of substance

g = gravitational constant = [tex]9.8 m/s^{2}[/tex]

h = height

Substitute the values into above formula as follows.

[tex]P.E = m \times g \times h\\67500 J = 4500 kg \times 9.8 m/s^{2} \times h\\h = \frac{67500 J}{4500 kg \times 9.8 m/s^{2}}\\= 1.53 m[/tex]

Hence, the height of rollercoaster cart above the ground is 1.53 m.

Kinetic energy is the energy occupied by the motion of a substance. Formula for kinetic energy is as follows.

[tex]K.E = \frac{1}{2}m \times v^{2}[/tex]

where,

m = mass of substance

v = velocity of substance

Substitute the values into above formula as follows.

[tex]K.E = \frac{1}{2}m \times v^{2}\\63000 J = \frac{1}{2} \times 4500 kg \times v^{2}\\v^{2} = \frac{63000 J \times 2}{4500 kg}\\v = 5.29 m/s[/tex]

Hence, the velocity of rollercoaster cart is 5.29 m/s.

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